Discrete Dynamics in Nature and Society

Volume 2018, Article ID 3093596, 10 pages

https://doi.org/10.1155/2018/3093596

## Short-Term Traffic Flow Forecasting Method Based on LSSVM Model Optimized by GA-PSO Hybrid Algorithm

College of Automobile and Transportation, Qingdao University of Technology, Qingdao 266520, China

Correspondence should be addressed to Dayi Qu; nc.ude.hcetq@uqiyad

Received 29 May 2018; Revised 9 October 2018; Accepted 5 November 2018; Published 15 November 2018

Academic Editor: Emilio Jiménez Macías

Copyright © 2018 Qichun Bing et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

Short-term traffic flow forecasting is one of the key issues in the field of dynamic traffic control and management. Because of the uncertainty and nonlinearity, short-term traffic flow forecasting remains a challenging task. In order to improve the accuracy of short-term traffic flow forecasting, a short-term traffic flow forecasting method based on LSSVM model optimized by GA-PSO hybrid algorithm is put forward. Firstly, the LSSVM model is constructed with combined kernel function. Then the GA-PSO hybrid optimization algorithm is designed to optimize the kernel function parameters efficiently and effectively. Finally, case validation is carried out using inductive loop data collected from the north-south viaduct in Shanghai. The experimental results demonstrate that the proposed GA-PSO-LSSVM model is superior to comparative method.

#### 1. Introduction

Real-time and accurate traffic flow forecasting information can provide the theoretical and data supports for the advanced traffic management system (ATMS) and advanced traffic information service system (ATIS). Because of its importance in both theoretical and empirical aspects of ITS, short-term traffic flow forecasting has generated great interest among researchers. With the development of traffic surveillance systems, more and more real-time traffic data become available in every couple of minutes or seconds. The short-term traffic flow forecasting generally means that the observation period is less than 15 minutes. The traffic flow forecasting, especially the short-term traffic flow forecasting, has been recognized as a critical need for the intelligent transportation systems. In the past decades, numerous studies have been applied to the traffic flow forecasting by researchers. The forecasting methods in the literatures can be broadly divided into parametric methods and nonparametric methods [1]. The parametric methods mainly include autoregressive integrated moving average (ARIMA) model [2–5], time series model [6–9], Kalman filtering model [10–13], parametric regressive model[14–16].This kind of method can get better forecasting effect if the traffic flow data varies temporally. However, these methods often assume a number of harsh conditions, such as the normality of residuals and a predefined model structure, which are seldom satisfied due to the stochastic and nonlinear characteristics of traffic flow. To overcome the limitations of parametric models, lots of researches have used nonparametric methods, such as nonparametric regressive model [17–19], spectral analysis model [20, 21], artificial neural networks (ANN) models [22–25], support vector machine (SVM) models [26–29], and so on. Particularly, the SVM model has great generalization ability and global minima for sample data, which has gained special attention in recent years. This paper is motivated to build the short-term traffic flow forecasting model based on SVM model due to its ability in dealing with the dynamic, nonlinear, and complex traffic flow time series.

Nevertheless, besides its advantages, there are some insufficiencies of the SVM based forecasting models. One is the choice of the kernel function. The traditional selection of kernel functions is single kernel function and generally dependents on experience. In view of this problem, we construct a combined kernel function to overcome the limitation of single kernel function. In addition, the parameters determination of SVM model remains a difficult yet important challenge. At present, the commonly used parameter optimization methods mainly include cross validation method [30] and grid search method [31]. But these methods are easy to fall into local optimum and have large amount of calculation. In order to obtain rational parameters, intelligent optimization algorithms have been pursued by many researchers. Particle swarm optimization (PSO) and genetic algorithm (GA) are the most popular intelligent optimization algorithms. Genetic algorithm (GA) [32] is a heuristic scientific method based on Darwin’s biological evolutionism, which can search parallel from a population of points. Therefore, it has the ability to avoid being trapped in local optimal solution. Particle swarm optimization (PSO) [33, 34] is a swarm intelligent optimization algorithm, which is derived from the study of bird predation behavior. Compared with genetic algorithm, the PSO algorithm has a simpler structure because it has no selection, crossover, and mutation operation. However, because the PSO algorithm evolves by comparing its own position and the surrounding position and the current optimal position in the group particle, therefore the convergence speed of the PSO algorithm is slow in the later calculation stage and easy to fall into local optimum value. Comparatively speaking, because of crossover, mutation, and other evolutionary patterns, GA can improve the diversity of solution. But GA often leads to a large number of redundant iterations when calculated to a certain extent, which reduces the computational efficiency.

Taking into account the above reasons and with the goal of improving the accuracy of short-term traffic flow forecasting, we put forward a short-term traffic flow forecasting method based on LSSVM model optimized by GA-PSO hybrid algorithm. The remainder of this paper is structured as follows: in section “Modeling of LSSVM Model”, the principle of LSSVM model and the construction of combined kernel function are presented. In section “GA-PSO Hybrid Optimization Algorithm Design”, the process of GA-PSO hybrid optimization algorithm is described. In section “Experiment Setup and Case Study”, empirical analysis is carried out, and the forecasting results of different approaches are presented and discussed. In section “Discussion and Conclusions”, a brief review and future research are presented.

#### 2. Modeling of LSSVM Model

##### 2.1. The Principle of LSSVM Model

LSSVM is an improved algorithm based on SVM. By introducing the method of equality constraint and least square loss function, the optimization problem is changed into a linear equation, and the complexity of the algorithm is reduced by avoiding the two programming problem. Regression forecasting based on LSSVM can be described as follows.

Considering a given training data set . The relationship between and is usually nonlinear, so is mapped into high-dimensional feature space. The regression function of LSSVM is defined as subject to

where* w *is the weight vector,* C *is the penalty factor, is the approximation error, is the nonlinear mapping function, and* b* is the offset. To solve the optimization problem, the Lagrange function can be introduced as follows:

where is the Lagrange multiplier. According to the Karush-Kuhn-Tucker(KKT) conditions, the following formula can be obtained by partial derivatives with respect to , , , and .

By eliminating and , the equations can be written as

where , , , and is kernel matrix with . Considering , the expressions of and can be written as

Therefore, the regression model of LSSVM can be obtained as

where is the kernel function which satisfies Mercer condition.

##### 2.2. The Construction of Combined Kernel Function

SVM model is built based on the principle of structural risk minimization, whose core idea is to introduce kernel functions. The SVM model with different kernel functions could have different learning and generalization ability. Therefore, how to select the appropriate kernel function is a major problem encountered in the field of short-term traffic flow forecasting.

At present, the commonly used kernel functions can be roughly divided into two categories, such as local kernel function and global kernel function. The Gaussian kernel function is typical local kernel function, which has strong learning ability and weak generalization ability. The polynomial kernel function is typical global kernel function, which has strong generalization ability and weak learning ability. Therefore, taking into account the advantages of Gaussian kernel function and polynomial kernel function, this paper will construct a new combination kernel function. The combination kernel function will not only have the local learning ability of Gauss kernel function but also has strong generalization ability of polynomial kernel function. The form of combination kernel function is as follows:

where is weight coefficient, , is the kernel width of Gaussian kernel function, and is the order of polynomial kernel function.

When approaches 0, the combined kernel function approximates the polynomial kernel function. Although it has good fitting ability to the sample data far away from the test point, the data fitting effect near the test point is poor. When approaches 1, the combined kernel function is close to the Gaussian kernel function, of which the global generalization ability is weak. In short, different kernel functions have different advantages, if the choice of weight coefficient is inappropriate, and the performance of combination kernel function may be lower than single kernel function. Therefore, proper weight coefficient is of great importance for the combined kernel function.

#### 3. GA-PSO Hybrid Optimization Algorithm Design

The construction of the combined kernel function increases the parameters that need to be optimized. This paper designs a new GA-PSO hybrid optimization algorithm to obtain the optimal parameters of LSSVM model. The main idea of the GA-PSO hybrid optimization algorithm is as follows: first of all, the PSO algorithm is carried out, and the optimal* M *particles are retained. Then,* pop*_*size-M* individuals are obtained by copying operations based on the position value of the* M* particles, and the crossover and mutation operations of GA are carried out. Finally, the position value of* M *particles retained by PSO and the* pop_size*-*M* obtained by GA form a new particle population and perform the next generation of evolutionary computing. Figure 1 gives the GA-PSO hybrid optimization schematic.